求数列1/3n(3n+2)的前n项和如题求数列1/3n*(3n+2)的前n项和是1/(3n(3n+2))

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求数列1/3n(3n+2)的前n项和如题求数列1/3n*(3n+2)的前n项和是1/(3n(3n+2))
求数列1/3n(3n+2)的前n项和
如题求数列1/3n*(3n+2)的前n项和
是1/(3n(3n+2))

求数列1/3n(3n+2)的前n项和如题求数列1/3n*(3n+2)的前n项和是1/(3n(3n+2))
(1/3)n(3n+2)
= (1/3)n(3n+3) - (1/3)n
= n(n+1) - n/3
= (1/3)[ n(n+1)(n+2) - (n-1)n(n+1) ] - (1/6)[ n(n+1) - (n-1)n ]
(1/3)n(3n+2)的前n项和
=(1/3)n(n+1)(n+2) - (1/6)n(n+1)
=(1/6)n(n+1)(2n+3)